Order = 322560 = 210.32.5.7.
Mult = 2.
Out = 1.
Porting notes
Fully copied from version 2. 30/7/06.Standard generators
Standard generators of 24.A8 are a, b where a is in class 3A, b has order 7, ab has order 6, [a, b] has order 2 and abab2ab5 has order 6. Alternatively: a is in class 3A, b has order 7, ab has order 6, ab3 has order 12 and abab2ab5 has order 6.
Standard generators of 24.2A8 are preimages A, B where A has order 3 and B has order 7.
Presentations
| Group | Presentation | Link |
|---|---|---|
| 24.A8 | 〈 a, b | a3 = b7 = (ab)6 = [a, b]2 = abab2a−1bab−2ab3ab−3ab−3 = 1 〉 | Details |
Representations
Representations of 24.A8
- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 30 Std Details 128 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 15 Std Details 2 GF(2) 11 a Std uniserial module 4.6.1 Details 2 GF(2) 11 b Std uniserial module 1.6.4 Details 3 GF(3) 15 Std Details 5 GF(5) 15 Std Details 7 GF(7) 15 Std Details